early 12c., "to strive toward, devote oneself to, cultivate" (translating Latin occupatur), from Old French estudiier "to study, apply oneself, show zeal for; examine" (13c., Modern French étudier), from Medieval Latin studiare, from Latin studium "study, application," originally "eagerness," from studere "to be diligent," from PIE *(s)teu- (1) "to push, stick, knock, beat" (see steep (adj.)). The notion appears to be "pressing forward, thrusting toward," hence "strive after."
Martha swanc and becarcade to geforðigene þan Hælende and his þeowen þa lichamlice behefðen. Seo studdede emb þa uterlice þing. [Homily for the Feast of the Virgin Mary, c.1125]
From c. 1300 as "apply oneself to the acquisition of learning, pursue a formal course of study," also "read a book or writings intently or meditatively." From mid-14c. as "reflect, muse, think, ponder." Meaning "regard attentively" is from 1660s. Related: Studied; studying.